Details

Time bar (total: 1.2m)

sample1.2s

Algorithm
intervals
Results
551.0ms125×body1280valid
261.0ms32×body5120valid
215.0ms71×body2560valid
73.0ms79×body640valid
49.0ms72×body80valid
24.0ms38×body320valid
8.0ms18×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: done (1.6s)

IterNodesCost
019941
144941
2149941
3856901
done5001860

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.8b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 2.0 (/ (pow t 3.0) (* l l)))
1.3b
(* (pow (/ k t) 2.0) (* (sin k) (tan k)))
15.6b
(/ (pow t 3.0) (* l l))
30.0b
(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
424×add-exp-log
226×div-exp
223×times-frac
141×prod-exp
82×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
77×add-cbrt-cube
58×pow-exp
49×unpow-prod-down
48×associate-/l*
40×pow-to-exp
34×cbrt-undiv
20×cbrt-unprod
17×associate-*l*
16×div-inv
13×associate-/r* sqr-pow
4×expm1-log1p-u pow1 associate-*r/ associate-/r/ log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×tan-quot
1×associate-*r* *-commutative associate-/l/
Counts
4 → 319
Calls
4 calls:
12.0ms
(/ 2.0 (/ (pow t 3.0) (* l l)))
57.0ms
(* (pow (/ k t) 2.0) (* (sin k) (tan k)))
18.0ms
(/ (pow t 3.0) (* l l))
61.0ms
(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))

series1.8s

Counts
4 → 12
Calls
4 calls:
368.0ms
(/ 2.0 (/ (pow t 3.0) (* l l)))
307.0ms
(* (pow (/ k t) 2.0) (* (sin k) (tan k)))
256.0ms
(/ (pow t 3.0) (* l l))
847.0ms
(/ (/ 2.0 (/ (pow t 3.0) (* l l))) (* (pow (/ k t) 2.0) (* (sin k) (tan k))))

simplify2.0s

Counts
331 → 331
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0471264824
11527246471
done5000243566

prune2.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (pow t 1.0) (pow k 2.0)))
0.6b
(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
8.4b
(* (pow t 1.0) (pow k 2.0))
15.0b
(* (* 2.0 (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))) (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
1298×add-exp-log
790×prod-exp
466×div-exp
367×pow-exp
157×pow-to-exp
80×rec-exp 1-exp
62×add-cbrt-cube
27×add-sqr-sqrt
23×cbrt-unprod
20×cbrt-undiv
19×unpow-prod-down
18×associate-*r*
15×*-un-lft-identity add-cube-cbrt
9×times-frac unswap-sqr sqr-pow
8×associate-*l*
6×associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r/ div-inv
2×clear-num associate-/r* frac-2neg associate-*l/ associate-*r/ *-commutative
1×frac-times pow-flip inv-pow
Counts
4 → 389
Calls
4 calls:
22.0ms
(/ 1 (* (pow t 1.0) (pow k 2.0)))
15.0ms
(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
19.0ms
(* (pow t 1.0) (pow k 2.0))
171.0ms
(* (* 2.0 (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))) (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
484.0ms
(/ 1 (* (pow t 1.0) (pow k 2.0)))
119.0ms
(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
426.0ms
(* (pow t 1.0) (pow k 2.0))
574.0ms
(* (* 2.0 (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))) (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0))

simplify2.9s

Counts
401 → 401
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0453380290
11322283874
done5001276514

prune1.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 7.5b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sin k) l) (/ (sin k) l))
0.4b
(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
0.6b
(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
15.0b
(* (* 2.0 (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))) (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0))

rewrite489.0ms

Algorithm
rewrite-expression-head
Rules
4232×add-exp-log
3008×prod-exp
1373×div-exp
1330×pow-exp
679×pow-to-exp
248×rec-exp 1-exp
76×add-cbrt-cube
51×add-sqr-sqrt
49×times-frac
39×*-un-lft-identity add-cube-cbrt
28×cbrt-unprod
25×cbrt-undiv
24×associate-*r*
14×associate-*l*
13×swap-sqr
12×pow1
7×unpow-prod-down div-inv
6×associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×associate-*l/ associate-*r/ associate-/r/
2×frac-times clear-num associate-/r* frac-2neg *-commutative
1×pow2 pow-plus pow-prod-down pow-sqr pow-prod-up pow-flip inv-pow sqr-pow
Counts
4 → 920
Calls
4 calls:
22.0ms
(* (/ (sin k) l) (/ (sin k) l))
53.0ms
(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
17.0ms
(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
249.0ms
(* (* 2.0 (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))) (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (/ (sin k) l) (/ (sin k) l))
500.0ms
(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
123.0ms
(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
597.0ms
(* (* 2.0 (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))) (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0))

simplify4.4s

Counts
932 → 932
Iterations

Useful iterations: done (4.1s)

IterNodesCost
0661990637
12151658506
done5000639226

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 6.6b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
0.6b
(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
4.0b
(* (* (* 2.0 (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))) (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))
9.7b
(* (* 2.0 (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))) (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
18430×add-exp-log
12565×prod-exp
7493×pow-exp
7102×div-exp
2675×pow-to-exp
1616×rec-exp 1-exp
102×add-cbrt-cube
47×cbrt-unprod
41×unpow-prod-down
40×associate-*r*
30×times-frac
29×cbrt-undiv
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×associate-/l*
5×pow1 sqr-pow
4×expm1-log1p-u associate-*l/ log1p-expm1-u div-inv add-log-exp
3×associate-*r/ associate-/r/
2×clear-num associate-/r* frac-2neg associate-*l* *-commutative
1×frac-times pow-flip inv-pow
Counts
4 → 3179
Calls
4 calls:
15.0ms
(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
24.0ms
(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
762.0ms
(* (* (* 2.0 (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))) (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))
185.0ms
(* (* 2.0 (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))) (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
521.0ms
(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
152.0ms
(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
595.0ms
(* (* (* 2.0 (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))) (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))
667.0ms
(* (* 2.0 (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))) (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0))

simplify9.0s

Counts
3191 → 3191
Iterations

Useful iterations: done (8.2s)

IterNodesCost
014944259434
done50002924832

prune2.5s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 6.4b

regimes1.1s

Accuracy

23.1% (5.3b remaining)

Error of 12.6b against oracle of 7.3b and baseline of 14.2b

bsearch3.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0422534
1502534
done502534

end0.0ms

sample31.0s

Algorithm
intervals
Results
8.8s4025×body1280valid
8.6s2196×body2560valid
7.5s952×body5120valid
3.4s2527×body640valid
990.0ms2009×body80valid
737.0ms947×body320valid
243.0ms437×body160valid